Synchronization of self-oscillator with fractional feedback

A model of self-oscillating system with a differential equation of motion of fractional order under the action of an external harmonic signal is proposed. Solutions of the equation of motion which correspond to the regime of steady-state synchronized oscillations and the regime of beats near the synchronization band are obtained in the quasiharmonic approximation. The amplitude frequency and phase-frequency characteristics of synchronization of fractional Van der Pol oscillator are analyzed. An analogy between the generator with a fractional feedback circuit and the generator with delayed feedback is established.